Algebra Examples

$45^{\frac{3}{2}} \cdot 45^{2}$

Step 1

Multiply $45^{\frac{3}{2}}$ by $45^{2}$ by adding the exponents.

Tap for more steps...

Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$45^{\frac{3}{2} + 2}$

Step 1.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$45^{\frac{3}{2} + 2 \cdot \frac{2}{2}}$

Step 1.3

Combine $2$ and $\frac{2}{2}$ .

$45^{\frac{3}{2} + \frac{2 \cdot 2}{2}}$

Step 1.4

Combine the numerators over the common denominator.

$45^{\frac{3 + 2 \cdot 2}{2}}$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $2$ by $2$ .

$45^{\frac{3 + 4}{2}}$

Step 1.5.2

Add $3$ and $4$ .

$45^{\frac{7}{2}}$

Step 2

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{45^{7}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{45^{7}}$

Decimal Form:

$611285.08334900 \dots$